{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Air density and gravity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rho = 1.225\n",
    "gravity = 9.81"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Drone"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Drone:\n",
    "\n",
    "    def __init__(self, init_z=5, init_v=0):\n",
    "        # Drone parameters\n",
    "        self.mass = 22.79e-3              # mass\n",
    "        self.D = 45e-3                    # radius\n",
    "        self.CT = 0.14                    # thrust coeff\n",
    "        self.Cd = 0.1                     # drag coeff\n",
    "        self.A = 0.01                     # total area\n",
    "        \n",
    "        # Control parameters\n",
    "        self.gain_pos = 0.5               # gain_pos\n",
    "        self.gain_vel = 0.7               # gain_vel\n",
    "        self.K = self.gain_pos*0.2*gravity\n",
    "        self.L = self.gain_vel*0.3*gravity\n",
    "        \n",
    "        # States\n",
    "        self.z = init_z                   # height\n",
    "        self.v = init_v                   # velocity\n",
    "        self.a = 0                        # acceleration\n",
    "        self.u = 0                        # control signal\n",
    "        \n",
    "        # Desired and actual force\n",
    "        self.Fd = 0\n",
    "        self.F = 0\n",
    "        \n",
    "        # Noise\n",
    "        self.a_noise_sigma = 0.5\n",
    "        self.u_noise_sigma = 30\n",
    "        self.a_noise = 0\n",
    "        self.u_noise = 0\n",
    "        \n",
    "        # Step\n",
    "        self.step_size = 1e-4\n",
    "        self.total_step = 0\n",
    "        \n",
    "    def position_controller(self, des_pos=0, des_vel=0):\n",
    "        ez = des_pos - self.z\n",
    "        dez = des_vel - self.v\n",
    "        \n",
    "        if (self.K*ez + gravity) > 0:\n",
    "            self.Fd = self.mass*(self.K*ez + gravity) + self.mass*self.L*dez \n",
    "        else:\n",
    "            self.Fd = self.mass*self.L*dez\n",
    "        \n",
    "        u_square = 1.0/(4*rho*self.D**4*self.CT)*self.Fd\n",
    "        if u_square < 0:\n",
    "            u_square = 0\n",
    "        \n",
    "        self.u = np.sqrt(u_square)\n",
    "\n",
    "    def dynamics(self):\n",
    "        # Noise freq is 100\n",
    "        if not self.total_step % 100: \n",
    "            self.a_noise = np.random.normal(0, self.a_noise_sigma)\n",
    "            self.u_noise = np.random.normal(0, self.u_noise_sigma)\n",
    "        \n",
    "        u = self.u + self.u_noise\n",
    "        \n",
    "        C_ground_effect = 1.0/(1 - 4*(0.5*self.D/(4*(0.05 + self.z)))**2)\n",
    "        self.F = 4*self.CT*C_ground_effect*rho*u**2*self.D**4\n",
    "        \n",
    "        self.a = self.F/self.mass - gravity - 0.5*rho*self.A*self.Cd*np.abs(self.v)*self.v/self.mass + self.a_noise\n",
    "        \n",
    "    def process(self):\n",
    "        self.position_controller()\n",
    "        self.dynamics()\n",
    "        self.z = self.z + self.step_size*self.v\n",
    "        self.v = self.v + self.step_size*self.a\n",
    "        self.total_step += 1\n",
    "    \n",
    "    def simulate(self, duration=10):\n",
    "        Height = []\n",
    "        Height = np.append(Height, self.z)\n",
    "        Velocity = []\n",
    "        Velocity = np.append(Velocity, self.v)\n",
    "        Control = []\n",
    "        Acceleration = []\n",
    "        while True:\n",
    "            self.process()\n",
    "            Height = np.append(Height, self.z)\n",
    "            Velocity = np.append(Velocity, self.v)\n",
    "            Control = np.append(Control, self.u)\n",
    "            Acceleration = np.append(Acceleration, self.a)\n",
    "            if not self.total_step % 1000:\n",
    "                print('Simulation time: ' + str(self.total_step*self.step_size))\n",
    "            if self.step_size*self.total_step >= duration:\n",
    "                break\n",
    "        return Height[:-1], Velocity[:-1], Control, Acceleration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Simulate():\n",
    "    drone = Drone()\n",
    "    Height, Velocity, Control, Acceleration = drone.simulate()\n",
    "    time = np.linspace(0.001,10,10e4)\n",
    "    plt.plot(time[:], Height)\n",
    "    plt.xlabel(\"time/s\")\n",
    "    plt.ylabel(\"height/m\")\n",
    "    plt.title(\"Height\")\n",
    "    # plt.savefig('height.png')\n",
    "    plt.show()\n",
    "    \n",
    "    plt.plot(time[:], Velocity)\n",
    "    plt.xlabel(\"time/s\")\n",
    "    plt.ylabel(\"velocity/m/s\")\n",
    "    plt.title(\"Velocity\")\n",
    "    # plt.savefig('velocity.png')\n",
    "    plt.show()\n",
    "    \n",
    "    plt.plot(time[:], Control)\n",
    "    plt.xlabel(\"time/s\")\n",
    "    plt.ylabel(\"control/rps\")\n",
    "    plt.title(\"Control\")\n",
    "    # plt.savefig('control.png')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulation time: 0.1\n",
      "Simulation time: 0.2\n",
      "Simulation time: 0.3\n",
      "Simulation time: 0.4\n",
      "Simulation time: 0.5\n",
      "Simulation time: 0.6\n",
      "Simulation time: 0.7000000000000001\n",
      "Simulation time: 0.8\n",
      "Simulation time: 0.9\n",
      "Simulation time: 1.0\n",
      "Simulation time: 1.1\n",
      "Simulation time: 1.2\n",
      "Simulation time: 1.3\n",
      "Simulation time: 1.4000000000000001\n",
      "Simulation time: 1.5\n",
      "Simulation time: 1.6\n",
      "Simulation time: 1.7000000000000002\n",
      "Simulation time: 1.8\n",
      "Simulation time: 1.9000000000000001\n",
      "Simulation time: 2.0\n",
      "Simulation time: 2.1\n",
      "Simulation time: 2.2\n",
      "Simulation time: 2.3000000000000003\n",
      "Simulation time: 2.4\n",
      "Simulation time: 2.5\n",
      "Simulation time: 2.6\n",
      "Simulation time: 2.7\n",
      "Simulation time: 2.8000000000000003\n",
      "Simulation time: 2.9000000000000004\n",
      "Simulation time: 3.0\n",
      "Simulation time: 3.1\n",
      "Simulation time: 3.2\n",
      "Simulation time: 3.3000000000000003\n",
      "Simulation time: 3.4000000000000004\n",
      "Simulation time: 3.5\n",
      "Simulation time: 3.6\n",
      "Simulation time: 3.7\n",
      "Simulation time: 3.8000000000000003\n",
      "Simulation time: 3.9000000000000004\n",
      "Simulation time: 4.0\n",
      "Simulation time: 4.1000000000000005\n",
      "Simulation time: 4.2\n",
      "Simulation time: 4.3\n",
      "Simulation time: 4.4\n",
      "Simulation time: 4.5\n",
      "Simulation time: 4.6000000000000005\n",
      "Simulation time: 4.7\n",
      "Simulation time: 4.8\n",
      "Simulation time: 4.9\n",
      "Simulation time: 5.0\n",
      "Simulation time: 5.1000000000000005\n",
      "Simulation time: 5.2\n",
      "Simulation time: 5.3\n",
      "Simulation time: 5.4\n",
      "Simulation time: 5.5\n",
      "Simulation time: 5.6000000000000005\n",
      "Simulation time: 5.7\n",
      "Simulation time: 5.800000000000001\n",
      "Simulation time: 5.9\n",
      "Simulation time: 6.0\n",
      "Simulation time: 6.1000000000000005\n",
      "Simulation time: 6.2\n",
      "Simulation time: 6.300000000000001\n",
      "Simulation time: 6.4\n",
      "Simulation time: 6.5\n",
      "Simulation time: 6.6000000000000005\n",
      "Simulation time: 6.7\n",
      "Simulation time: 6.800000000000001\n",
      "Simulation time: 6.9\n",
      "Simulation time: 7.0\n",
      "Simulation time: 7.1000000000000005\n",
      "Simulation time: 7.2\n",
      "Simulation time: 7.300000000000001\n",
      "Simulation time: 7.4\n",
      "Simulation time: 7.5\n",
      "Simulation time: 7.6000000000000005\n",
      "Simulation time: 7.7\n",
      "Simulation time: 7.800000000000001\n",
      "Simulation time: 7.9\n",
      "Simulation time: 8.0\n",
      "Simulation time: 8.1\n",
      "Simulation time: 8.200000000000001\n",
      "Simulation time: 8.3\n",
      "Simulation time: 8.4\n",
      "Simulation time: 8.5\n",
      "Simulation time: 8.6\n",
      "Simulation time: 8.700000000000001\n",
      "Simulation time: 8.8\n",
      "Simulation time: 8.9\n",
      "Simulation time: 9.0\n",
      "Simulation time: 9.1\n",
      "Simulation time: 9.200000000000001\n",
      "Simulation time: 9.3\n",
      "Simulation time: 9.4\n",
      "Simulation time: 9.5\n",
      "Simulation time: 9.6\n",
      "Simulation time: 9.700000000000001\n",
      "Simulation time: 9.8\n",
      "Simulation time: 9.9\n",
      "Simulation time: 10.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/GuanyaShi/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:4: DeprecationWarning: object of type <class 'float'> cannot be safely interpreted as an integer.\n",
      "  after removing the cwd from sys.path.\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a6010b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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QHecYXFbvqaK9w015Q1cJkTvPm8vJMzVZKBUuEUscxpiTe3tMREpFZKTd2hgJ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\nO1gVcXOx9uC4wuntWweKSbl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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a5e9ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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6x3uEtVLj6Yz8OYpJcNUO0lX1MY+X9gOnAYuB2cB2p/wd4Gci8gquzuni7tL/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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a5b0da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Simulate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
